My SIL and I just do not get along that well and are mostly formal with each other. But now that I am pregnant, I want things to be good for my baby in the future. How do I initiate a discussion with her?

Find something the both of you like to do and do it together. Maybe go baby shopping together? Go for lunches and just hang out together. Start small, have regular dates and I'm sure the bond of sisterhood will grow :) good luck!